LEVY-KHINTCHINE REPRESENTATION OF THE GEOMETRIC MEAN OF MANY POSITIVE NUMBERS AND APPLICATIONS

被引：18

作者：

Qi, Feng ^{[1
,2
]}

Zhang, Xiao-Jing ^{[3
,4
]}

Li, Wen-Hui ^{[4
]}

机构：

[1] Henan Polytech Univ, Inst Math, Jiaozuo City 454010, Henan Province, Peoples R China

[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China

[3] 59th Middle Sch, Luoyang City 471000, Henan Province, Peoples R China

[4] Tianjin Polytech Univ, Sch Sci, Dept Math, Tianjin 300387, Peoples R China

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2014年 / 17卷 / 02期

关键词：

Levy-Khintchine representation; integral representation; geometric mean; completely monotonic function; logarithmically completely monotonic function; Bernstein function; complete Bernstein function; Cauchy integral formula; arithmetic-geometric mean inequality; COMPLETE MONOTONICITY; GAMMA; PROPERTY;

D O I：

10.7153/mia-17-53

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper, the authors establish, by Cauchy integral formula in the theory of complex functions, Levy-Khintchine representation for the geometric mean of many positive numbers, find that the geometric mean of many positive numbers is a complete Bernstein function, and supply a new proof of the well known arithmetic-geometric mean inequality.

引用

页码：719 / 729

页数：11